1. Lab # 5: Convection Heat Transfer Max Tenorio
14:650:432:02
Lab # 5: Convection Heat Transfer
Max Tenorio

2. Purpose Convection Heat Transfer occurs almost everywhere
Examine characteristics of heat transfer to turbulent air flow through a uniformly heated pipe
Measure temperature distribution for two air flow rates and two power settings to calculate the heat transfer coefficient, Reynolds, Stanton, and Prandtl numbers and friction factor.

3. Setup

4. Specifications Total 5.75 feet long Insulation thickness: 0.813”
13 total thermocouples (1 broken)
Connected to labview

5. Raw Data Units Run - 1 2 3 4 Current A 2.5 Voltage V 140 210 135
Run - 1 2 3 4
Current A
2.5
Voltage V
140
210
135
Pa fan
inH2O
13.2
3.9
Pb plate
3.5
0.9
Pc test sec
2.7
3.1
1.1 T1 C
49.284 98 T2
51.681
77.642 T3
53.486 T4
54.358
83.922 T5
55.261
71.821
123.37 T6
56.692 T7
66.038 T8
72.319 T9
24.662
T10
T11
T12
74.716
T13
25.035
Ttest section 37
48.5 38 39
Tamb 20
Pbarom
atm

6. Mass Flow Rate Run 1 Run 2 Run 3 Run 4 Mass Flow Rate (kg/s)
Volume Flow Rate (L/s)
Run 1
Run 2
Run 3
Run 4

7. Heat Flux Method 1 q" in q"loss avg q" heat flux Run W/m^2 1 1949.11
460.94 2
986.90 3
533.59 4

8. Thermal Profile

9. Heat Flux Method 2 Requires Thermal Profiles
Discussion b: The heat flux values in b and d are different because b uses raw experimental values to perform the heat balance and assumes that for q”out, the maximum heat loss is uniform for the entire circumference for the pipe, when in reality the heat loss is most likely not uniform through a cross section. Additionally, d assumes laminar flow and relies on a constant specific heat capacity for air and a constant flow rate.
dTs(x)/dx
q" (b)
q" in (b)
q"(d)
assuming b is correct
Run
°K/m
W/m^2
% error 1
5.2741 2
12.672 3
9.1567
1879.5 4
21.183
Although the percent error is somewhat high, it is worth noting that the heat flux from d is close to the q”in from b. The difference is most likely equipment error and incorrect values

10. Bulk Air Temperature
The Bulk Air temperature is the average temperature of air in a section of pipe. Tx
x (m) 1 2 3 4
0.3175
38.25
51.60
40.07
44.24
39.81
55.48
42.66
50.78
1.0287
41.05
58.55
44.70
55.97
41.72
60.20
45.80
58.74
42.38
61.84
46.90
61.52
43.04
63.49
47.99
64.29
1.7018
43.71
65.13
49.09
67.07

11. Heat Transfer Coefficient1 2 3 4 h3 h4 h5
54.002
havg
154.84
55.123
Discussion a: The wall temperature is easily measured using the thermocouples and the bulk temperature is the average temperature of air in that cross section. They vary; the wall temperature will be higher because it is closer to the heating element and the temperatures are higher in general because energy is being transferred to the air as it travels. The beginning and end points are skewed because of end effects. The slopes of both are constant in the middle section because the rate at which temperature changes is the same for both the wall and air inside the tube.

12. Reynolds Number
Ratio of inertial forces (Vρ) to viscous forces (μ / L)
Reynolds Number
Run 1
Run 2
Run 3
Run 4

13. Nusselt Number
Ratio of convective to conductive heat transfer across the boundary
Correlation
Regular
Run 1
229.13
153.48
Run 2
202.00
Run 3
141.36
71.91
Run 4
145.18
75.33

14. Friction factor Correlation Regular Run 1 0.017161 0.004274 Run 2
Run 3
Run 4

15. Stanton Number
Ratio of heat transferred into a fluid to the thermal capacity of fluid
Correlation
Regular
Run 1
Run 2
Run 3
Run 4

16. Calculated Values Re
q“ (w/m^2K)
Nu, exp.
Nu, corr.
f, exp.
f, corr
St, exp.
St, corr.
Run 1
153.48
229.13
Run 2
202.00
Run 3
71.91
141.36
Run 4
75.33
145.18
Discussion c: For the Nusselt Number and friction factor, the experimental values are much lower than the correlation values. These most likely result from equipment error, since the friction factors for runs 3 and 4 drop to zero and even go negative, meaning the pressure at the exit is higher than the entrance pressure. As far as the Stanton number goes, the values for the high speed regions (runs 1 and 2) are close, but the values for low speed are off, meaning that less energy was transferred into the air than anticipated.

17. Sample Calculations Run 1 Pa Fan Pb Plate Δh (m) A (m^2) g (m/s^2)
Air Density (kg/m^3)
Water Density (kg/m^3)
Flow Coefficient
Mass Flow Rate (kg/s) 1
0.0889
9.8
0.6 T8
T10
T12 T9
T11
T13
ΔT1
ΔT2
ΔT3 R
q" loss 1
q" loss 2
q" loss 3
q"loss avg C
m^2K/W
W/m^2 1
72.319
74.716
24.662
25.035
47.657
49.681
Mass Flow Rate pi cp Di
dTs(x)/dx
q"
kg/s
J/kgK m
°K/m
W/m^2 1
1012
5.2741
x (m) Ts Tx
Ts(x) - T(x)
h (W/M^2K)
0.3175
49.284
38.251
11.033
51.681
1.0287
53.486
54.358
55.261
56.692
1.7018
66.038

18. Sample Calculations Re 1 Re=QD/VA Q 0.046171197 D 0.0326136 ν 1.57E-05 Pr
ν/α α
2.22E-05
7.08E-01 Nu
Nu=0.023*Re^0.8*Pr^1/3
Nu=hD/k h k
0.025
Friction factor f p1 p2
air density
mass flow rate L
1.7526
Equation
Stanton Number
Correlation St
St=h/ρcpV